Functional Controllability, Functional Stabilizability, and the Generalized Separation Principle

TL;DR

This paper introduces the concepts of Functional Controllability and Stabilizability, establishing their duality with observability, and presents a generalized separation principle that extends classical control design methods.

Contribution

It develops a new control framework based on functional properties, allowing controller design without full controllability and extending classical observer-based control.

Findings

Conditions for functional controller existence derived

Framework does not require full controllability

Extends classical observer-based control paradigm

Abstract

This paper introduces the new concepts of Functional Controllability and Functional Stabilizability, and establishes their duality with Functional Observability and Functional Detectability, respectively. A Generalized Separation Principle is presented, under which the classical Separation Principle emerges as a special case. Conditions for the existence of functional controllers of a specified order are derived. Notably, the proposed design framework does not require full controllability. In addition, a functional observer-based controller design is developed for systems that may be both uncontrollable and unobservable. The results presented extend and generalize the classical full-state observer based feedback control paradigm.